[Maximum number: 5]

The first three terms of an infinite geometric sequence are 32,16 and 8 .

(a)

Write down the value of r.

[ 1 ]

(b)

Find $u_{6}$ .

[ 2 ]

(c)

Find the sum to infinity of this sequence.

[ 2 ]

[Maximum number: 6]

In an arithmetic sequence, the first term is 3 and the second term is 7 .

(a)

Find the common difference.

[ 2 ]

(b)

Find the tenth term.

[ 2 ]

(c)

Find the sum of the first ten terms of the sequence.

[ 2 ]

[Maximum number: 6]

The first three terms of an arithmetic sequence are $u_{1}=0.3, u_{2}=1.5, u_{3}=2.7$ .

(a)

Find the common difference.

[ 2 ]

(b)

Find the 30th term of the sequence.

[ 2 ]

(c)

Find the sum of the first 30 terms.

[ 2 ]

[Maximum number: 5]

Write each of the following expressions in the form $\ln k$ , where $k \in \mathbb{Z}^{+}$ .

(a)

$\ln 3+\ln 4$

[ 1 ]

(b)

$3 \ln 2$

[ 2 ]

(c)

$-\ln \frac{1}{2}$

[ 2 ]

[Maximum number: 12]

The first three terms of an arithmetic sequence are $36,40,44, \ldots$ .

(a)

(i)

Write down the value of d.

[ 3 ]

(ii)

Find $u_{8}$ .

[ 3 ]

(b)

(i)

Show that $S_{n}=2 n^{2}+34 n$ .

[ 3 ]

(ii)

Hence, write down the value of $S_{14}$ .

[ 3 ]

[Maximum number: 4]

The second term of an arithmetic sequence is 10 and the fourth term is 22.

(a)

Find the value of the common difference.

[ 2 ]

(b)

Find an expression for $u_{n}$ , the nth term.

[ 2 ]

[Maximum number: 7]

An arithmetic sequence is given by $5,8,11, \ldots$ .

(a)

Write down the value of d.

[ 1 ]

(b)

Find

[ 4 ]

(i)

$u_{100}$ ;

(ii)

$S_{100} \cdot$

[ 4 ]

(c)

Given that $u_{n}=1502$ , find the value of n.

[ 2 ]

[Maximum number: 6]

The first three terms of an arithmetic sequence are 5,6.7,8.4.

(a)

Find the common difference.

[ 2 ]

(b)

Find the $28^{\text {th }}$ term of the sequence.

[ 2 ]

(c)

Find the sum of the first 28 terms.

[ 2 ]

[Maximum number: 1]

In this question, give all answers correct to two decimal places.
Sam invests $ 1700 in a savings account that pays a nominal annual rate of interest of 2.74 %, compounded half-yearly. Sam makes no further payments to, or withdrawals from, this account.

(a)

Find the interest David will earn over the 10 years.

[ 1 ]

[Maximum number: 6]

In an arithmetic sequence, $u_{1}=2$ and $u_{3}=8$ .

(a)

Find d.

[ 2 ]

(b)

Find $u_{20}$ .

[ 2 ]

(c)

Find $S_{20}$ .

[ 2 ]

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